In this talk, we present a locally mass-conservative finite element method based on enriching the approximation space of the continuous Galerkin (CG) method with elementwise constant functions. The proposed method has a smaller number of degrees of freedom than the discontinuous Galerkin (DG) method. Numerical results on coupled flow and transport problems in porous media are provided to illustrate the advantages of this method. Optimal error estimates of the EG method and comparison with related post-processing methods will be discussed also. This is a joint work with Shuyu Sun at Clemson University.